# Information Dynamics of Electric Field Intensity before and during the COVID-19 Pandemic

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. EMF RATEL Monitoring System and EF Intensity Time Series

#### 2.2. Time Series Pre-Processing

#### 2.3. Information-Theoretic Analysis

#### 2.4. Estimation of the Information Storage

#### 2.5. Surrogate Data Analysis

## 3. Results and Discussion

## 4. Conclusions and Future Perspectives

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Presman, A. Electromagnetic Fields and Life; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2013. [Google Scholar]
- Goldsmith, A. Wireless Communications; Cambridge University Press: Cambridge, MA, USA, 2005. [Google Scholar]
- Wong, V.W.; Schober, R.; Ng, D.W.K.; Wang, L.C. Key Technologies for 5G Wireless Systems; Cambridge University Press: Cambridge, MA, USA, 2017. [Google Scholar]
- Saad, W.; Bennis, M.; Chen, M. A vision of 6G wireless systems: Applications, trends, technologies, and open research problems. IEEE Netw.
**2019**, 34, 134–142. [Google Scholar] [CrossRef][Green Version] - Zhang, M.; Raghunathan, A.; Jha, N.K. MedMon: Securing medical devices through wireless monitoring and anomaly detection. IEEE Trans. Biomed. Circuits Syst.
**2013**, 7, 871–881. [Google Scholar] [CrossRef] [PubMed] - Bor-Yaliniz, I.; Salem, M.; Senerath, G.; Yanikomeroglu, H. Is 5G ready for drones: A look into contemporary and prospective wireless networks from a standardization perspective. IEEE Wirel. Commun.
**2019**, 26, 18–27. [Google Scholar] [CrossRef] - Cheng, X.; Zhang, R.; Yang, L. Wireless toward the era of intelligent vehicles. IEEE Internet Things J.
**2018**, 6, 188–202. [Google Scholar] [CrossRef] - Scientific Committee on Emerging Newly Identified Health Risks. Opinion on potential health effects of exposure to electromagnetic fields. Bioelectromagnetics
**2015**, 36, 480–484. [Google Scholar] [CrossRef] - International Commission on Non-Ionizing Radiation Protection (ICNRP). Guidelines for limiting exposure to electromagnetic fields (100 KHz to 300 GHz). Health Phys.
**2020**, 118, 483–524. [Google Scholar] [CrossRef] - Gonzalez, M.C.; Hidalgo, C.A.; Barabasi, A.L. Understanding individual human mobility patterns. Nature
**2008**, 453, 779–782. [Google Scholar] [CrossRef] - Song, C.; Qu, Z.; Blumm, N.; Barabási, A.L. Limits of predictability in human mobility. Science
**2010**, 327, 1018–1021. [Google Scholar] [CrossRef][Green Version] - Onnela, J.P.; Saramäki, J.; Hyvönen, J.; Szabó, G.; Lazer, D.; Kaski, K.; Kertész, J.; Barabási, A.L. Structure and tie strengths in mobile communication networks. Proc. Natl. Acad. Sci. USA
**2007**, 104, 7332–7336. [Google Scholar] [CrossRef][Green Version] - Phithakkitnukoon, S.; Smoreda, Z.; Olivier, P. Socio-geography of human mobility: A study using longitudinal mobile phone data. PLoS ONE
**2012**, 7, e39253. [Google Scholar] [CrossRef][Green Version] - Eagle, N.; Macy, M.; Claxton, R. Network diversity and economic development. Science
**2010**, 328, 1029–1031. [Google Scholar] [CrossRef] [PubMed] - Chu, D.K.; Akl, E.A.; Duda, S.; Solo, K.; Yaacoub, S.; Schünemann, H.J.; El-harakeh, A.; Bognanni, A.; Lotfi, T.; Loeb, M.; et al. Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19: A systematic review and meta-analysis. Lancet
**2020**, 395, 1973–1987. [Google Scholar] [CrossRef] - Welsch, R.; Wessels, M.; Bernhard, C.; Thönes, S.; von Castell, C. Physical distancing and the perception of interpersonal distance in the COVID-19 crisis. Sci. Rep.
**2021**, 11, 1–9. [Google Scholar] [CrossRef] [PubMed] - Lizier, J.T.; Prokopenko, M.; Zomaya, A.Y. Local measures of information storage in complex distributed computation. Inf. Sci.
**2012**, 208, 39–54. [Google Scholar] [CrossRef] - Wibral, M.; Lizier, J.; Vögler, S.; Priesemann, V.; Galuske, R. Local active information storage as a tool to understand distributed neural information processing. Front. Neuroinform.
**2014**, 8, 1. [Google Scholar] [CrossRef][Green Version] - Kitzbichler, M.G.; Smith, M.L.; Christensen, S.R.; Bullmore, E. Broadband criticality of human brain network synchronization. PLoS Comput. Biol.
**2009**, 5, e1000314. [Google Scholar] [CrossRef][Green Version] - Ay, N.; Bertschinger, N.; Der, R.; Güttler, F.; Olbrich, E. Predictive information and explorative behavior of autonomous robots. Eur. Phys. J. B
**2008**, 63, 329–339. [Google Scholar] [CrossRef][Green Version] - Faes, L.; Porta, A.; Nollo, G. Information decomposition in bivariate systems: Theory and application to cardiorespiratory dynamics. Entropy
**2015**, 17, 277–303. [Google Scholar] [CrossRef] - Faes, L.; Porta, A.; Nollo, G.; Javorka, M. Information decomposition in multivariate systems: Definitions, implementation and application to cardiovascular networks. Entropy
**2017**, 19, 5. [Google Scholar] [CrossRef] - Xiong, W.; Faes, L.; Ivanov, P.C. Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations. Phys. Rev. E
**2017**, 95, 062114. [Google Scholar] [CrossRef][Green Version] - Theiler, J.; Eubank, S.; Longtin, A.; Galdrikian, B.; Farmer, J.D. Testing for nonlinearity in time series: The method of surrogate data. Phys. D Nonlinear Phenom.
**1992**, 58, 77–94. [Google Scholar] [CrossRef][Green Version] - Costa, M.; Goldberger, A.L.; Peng, C.K. Multiscale entropy analysis of biological signals. Phys. Rev. E
**2005**, 71, 021906. [Google Scholar] [CrossRef] [PubMed][Green Version] - The EMF RATEL Internet Portal. Available online: https://emf.ratel.rs/ (accessed on 29 March 2022).
- Djuric, N.; Kavecan, N.; Mitic, M.; Radosavljevic, N. The EMF RATEL Service for Monitoring and Public Informing on EMF Exposure. In Proceedings of the IEEE INFOCOM 2019-IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), Paris, France, 29 April–2 May 2019; pp. 909–910. [Google Scholar]
- Serbian Open Data Portal. Available online: https://data.gov.rs/sr/datasets/rezultati-kontinualnog-merenja-nivoa-elektrichnog-polja-na-lokatsijama-od-interesa (accessed on 3 May 2022).
- Serbian Open Data Portal. Available online: https://emf.ratel.rs/getOpenData/4/csv (accessed on 3 May 2022).
- Faes, L.; Porta, A.; Javorka, M.; Nollo, G. Efficient computation of multiscale entropy over short biomedical time series based on linear state-space models. Complexity
**2017**, 2017, 1768264. [Google Scholar] [CrossRef] - Nollo, G.; Faes, L.; Pellegrini, B.; Porta, A.; Antolini, R. Synchronization index for quantifying nonlinear causal coupling between RR interval and systolic arterial pressure after myocardial infarction. In Proceedings of the Computers in Cardiology 2000, (Cat. 00CH37163), Cambridge, MA, USA, 24–27 September 2000; Volume 27, pp. 143–146. [Google Scholar]
- Cover, T.M. Elements of Information Theory; John Wiley & Sons: Hoboken, NJ, USA, 1999. [Google Scholar]
- Faes, L.; Pereira, M.A.; Silva, M.E.; Pernice, R.; Busacca, A.; Javorka, M.; Rocha, A.P. Multiscale information storage of linear long-range correlated stochastic processes. Phys. Rev. E
**2019**, 99, 032115. [Google Scholar] [CrossRef][Green Version] - Richman, J.S.; Moorman, J.R. Physiological time-series analysis using approximate entropy and sample entropy. Am. J.-Physiol.-Heart Circ. Physiol.
**2000**, 278, H2039–H2049. [Google Scholar] [CrossRef][Green Version] - Faes, L.; Porta, A.; Rossato, G.; Adami, A.; Tonon, D.; Corica, A.; Nollo, G. Investigating the mechanisms of cardiovascular and cerebrovascular regulation in orthostatic syncope through an information decomposition strategy. Auton. Neurosci.
**2013**, 178, 76–82. [Google Scholar] [CrossRef] - Kozachenko, L.; Leonenko, N.N. Sample estimate of the entropy of a random vector. Probl. Peredachi Inf.
**1987**, 23, 9–16. [Google Scholar] - Kraskov, A.; Stögbauer, H.; Grassberger, P. Estimating mutual information. Phys. Rev. E
**2004**, 69, 066138. [Google Scholar] [CrossRef][Green Version] - Schreiber, T.; Schmitz, A. Surrogate time series. Phys. D Nonlinear Phenom.
**2000**, 142, 346–382. [Google Scholar] [CrossRef][Green Version] - Schreiber, T.; Schmitz, A. Improved surrogate data for nonlinearity tests. Phys. Rev. Lett.
**1996**, 77, 635. [Google Scholar] [CrossRef][Green Version] - Faes, L.; Gómez-Extremera, M.; Pernice, R.; Carpena, P.; Nollo, G.; Porta, A.; Bernaola-Galván, P. Comparison of methods for the assessment of nonlinearity in short-term heart rate variability under different physiopathological states. Chaos Interdiscip. J. Nonlinear Sci.
**2019**, 29, 123114. [Google Scholar] [CrossRef] [PubMed][Green Version] - The Government of the Republic of Serbia. Available online: https://www.srbija.gov.rs/vest/en/151422/measures-of-the-state-of-emergency.php (accessed on 29 March 2022).
- The EMF RATEL Internet Portal. Available online: https://emf.ratel.rs/results/details/eng/9/ (accessed on 3 May 2022).
- Kljajic, D.; Djuric, N. Comparative analysis of EMF monitoring campaigns in the campus area of the University of Novi Sad. Environ. Sci. Pollut. Res.
**2020**, 27, 14735–14750. [Google Scholar] [CrossRef] [PubMed] - Li, A.; Zhao, P.; Haitao, H.; Mansourian, A.; Axhausen, K.W. How did micro-mobility change in response to COVID-19 pandemic: A case study based on spatial-temporal-semantic analytics. Comput. Environ. Urban Syst.
**2021**, 90, 101703. [Google Scholar] [CrossRef] [PubMed] - Fonseca-Cabrera, A.S.S.; Llopis-Castelló, D.; Pérez-Zuriaga, A.M.M.; Alonso-Troyano, C.; García, A. Micromobility Users’ Behaviour and Perceived Risk during Meeting Manoeuvres. Int. J. Environ. Res. Public Health
**2021**, 18, 12465. [Google Scholar] [CrossRef] [PubMed] - Albino, V.; Berardi, U.; Dangelico, R.M. Smart cities: Definitions, dimensions, performance, and initiatives. J. Urban Technol.
**2015**, 22, 3–21. [Google Scholar] [CrossRef]

**Figure 1.**Representative time series of EF intensity monitored during the same day (

**a**), week (

**b**), and month (

**c**) of 2019 (orange) and 2020 (green), as well as during the whole years 2019 and 2020 (

**d**). The time series samples are obtained averaging the EF intensity over a time scale that is peculiar of each observation window: ${\tau}_{day}=6$ min in (

**a**); ${\tau}_{week}=30$ min in (

**b**); ${\tau}_{month}=2$ h in (

**c**); ${\tau}_{year}=1$ day in (

**d**).

**Figure 2.**Mean of the EF intensity time series computed over observation windows lasting one day at the time scale ${\tau}_{day}=6$ min (

**a**), one week at the time scale ${\tau}_{week}=30$ min (

**b**), one month at the time scale ${\tau}_{month}=2$ h (

**c**), and one year at the time scale ${\tau}_{year}=1$ day (

**d**). The colored areas identify periods of different activities in the campus area of the University of Novi Sad, occurring before (2019) and during (2020) the COVID-19 pandemic. The colored areas may differ slightly between the two analyzed years (±a few days).

**Figure 3.**Variance of the EF intensity time series computed over observation windows lasting one day at the time scale ${\tau}_{day}=6$ min (

**a**), one week at the time scale ${\tau}_{week}=30$ min (

**b**), one month at the time scale ${\tau}_{month}=2$ h (

**c**), and one year at the time scale ${\tau}_{year}=1$ day (

**d**). The colored areas identify periods of different activities in the campus area of the University of Novi Sad, occurring before (2019) and during (2020) the COVID-19 pandemic. The colored areas may differ slightly between the two analyzed years (±a few days).

**Figure 4.**Information storage computed on the representative time series reported in Figure 1 (filled symbols, positioned left) and on 100 IAAFT surrogates (empty circles, right). The thresholds set to detect statistically significant nonlinear dynamics are indicated by blue lines; time series with significant nonlinearity are detected when the original $IS$ exceeds the threshold level (orange or green circles), while the time series is regarded as linear when the original $IS$ is below the threshold (black squares).

**Figure 5.**Information storage of the EF intensity time series computed over observation windows lasting one day at the time scale ${\tau}_{day}=6$ min (

**a**), one week at the time scale ${\tau}_{week}=30$ min (

**b**), one month at the time scale ${\tau}_{month}=2$ h (

**c**), and one year at the time scale ${\tau}_{year}=1$ day (

**d**). The colored areas identify periods of different activities in the campus area of the University of Novi Sad, occurring before (2019) and during (2020) the COVID-19 pandemic. The colored areas may differ slightly between the two analyzed years (±a few days). Black-colored squares indicate the presence of linear dynamics, while orange (2019) and green (2020) circles the presence of nonlinear dynamics, detected through the method of surrogate data.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mijatovic, G.; Kljajic, D.; Kasas-Lazetic, K.; Milutinov, M.; Stivala, S.; Busacca, A.; Cino, A.C.; Stramaglia, S.; Faes, L.
Information Dynamics of Electric Field Intensity before and during the COVID-19 Pandemic. *Entropy* **2022**, *24*, 726.
https://doi.org/10.3390/e24050726

**AMA Style**

Mijatovic G, Kljajic D, Kasas-Lazetic K, Milutinov M, Stivala S, Busacca A, Cino AC, Stramaglia S, Faes L.
Information Dynamics of Electric Field Intensity before and during the COVID-19 Pandemic. *Entropy*. 2022; 24(5):726.
https://doi.org/10.3390/e24050726

**Chicago/Turabian Style**

Mijatovic, Gorana, Dragan Kljajic, Karolina Kasas-Lazetic, Miodrag Milutinov, Salvatore Stivala, Alessandro Busacca, Alfonso Carmelo Cino, Sebastiano Stramaglia, and Luca Faes.
2022. "Information Dynamics of Electric Field Intensity before and during the COVID-19 Pandemic" *Entropy* 24, no. 5: 726.
https://doi.org/10.3390/e24050726